An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries

A Cartesian grid method has been developed for simulating two-dimensional u nsteady, viscous, incompressible flows with complex immersed boundaries. A finite-volume method based on a second-order accurate central-difference sc heme is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a solver are impo sition of boundary conditions on the immersed boundaries and accurate discr etization of the governing equation in cells that are cut by these boundari es. A new interpolation procedure is presented which allows systematic deve lopment of a spatial discretization scheme that preserves the second-order spatial accuracy of the underlying solver. The presence of immersed boundar ies alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated b y using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accur acy and fidelity of the solver is validated by simulating a number of canon ical flows and the ability of the solver to simulate flows with very compli cated immersed boundaries is demonstrated. (C) 1999 Academic Press.